00:01
The area a of the region s that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles.
00:14
A equal limit when n goes to infinity of rn.
00:19
That is the limit when n goes to infinity of f at x1 times delta x plus f at x2 plus delta times delta x plus up to f at xx times delta x plus up to f at xx times delta x plus up to f at x n times delta.
00:32
We consider a function square root, sorry, a fourth root of x for x greater than equal to 1 and less than equal to 16.
00:44
Using the above definition, determine which of the following represents the area under the graph of f as a limit.
00:52
So we have four options and we're going to calculate the formula, which is the approximation to the area and for which we're we take the limit when n goes to infinity.
01:08
So we have the interval 116, that's the interval of integration, because it's been said here.
01:17
The function is fourth root of x, or x to the one -fourth, that's the same, which is well defined here because being the index of the root and even number, the expression under the square, under the root, get a big positive or zero, and that's true for all bodies of x in the interval 116.
01:48
So to calculate the area of the rectangle, the approximating rectangles, we get to calculate a partition of n sub -intervals of equal length, of equal length on 116.
02:18
And so if we have n sub intervals of equal length on that interval 116, we can calculate the length of any of these sub intervals.
02:32
We've got to be the same.
02:33
And that value is, let's call it h, usually call step size, is 16 minus 1 over n...